On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
On Friday, April 12, 2019 at 5:48:23 AM UTC-6,
agrays...@gmail.com wrote:
On Thursday, April 11, 2019 at 10:56:08 PM UTC-6,
Brent wrote:
On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
On Thursday, April 11, 2019 at 7:12:17 PM
UTC-6, Brent wrote:
On 4/11/2019 4:53 PM, agrays...@gmail.com
wrote:
On Thursday, April 11, 2019 at 4:37:39 PM
UTC-6, Brent wrote:
On 4/11/2019 1:58 PM,
agrays...@gmail.com wrote:
He might have been referring to
a transformation to a tangent
space where the metric tensor is
diagonalized and its derivative
at that point in spacetime is
zero. Does this make any sense?
Sort of.
Yeah, that's what he's doing. He's
assuming a given coordinate system
and some arbitrary point in a
non-empty spacetime. So spacetime has
a non zero curvature and the
derivative of the metric tensor is
generally non-zero at that arbitrary
point, however small we assume the
region around that point. But
applying the EEP, we can transform to
the tangent space at that point to
diagonalize the metric tensor and
have its derivative as zero at that
point. Does THIS make sense? AG
Yep. That's pretty much the defining
characteristic of a Riemannian space.
Brent
But isn't it weird that changing labels on
spacetime points by transforming
coordinates has the result of putting the
test particle in local free fall, when it
wasn't prior to the transformation? AG
It doesn't put it in free-fall. If the
particle has EM forces on it, it will
deviate from the geodesic in the tangent
space coordinates. The transformation is
just adapting the coordinates to the local
free-fall which removes gravity as a
force...but not other forces.
Brent
In both cases, with and without
non-gravitational forces acting on test
particle, I assume the trajectory appears
identical to an external observer, before and
after coordinate transformation to the tangent
plane at some point; all that's changed are the
labels of spacetime points. If this is true,
it's still hard to see why changing labels can
remove the gravitational forces. And what does
this buy us? AG
You're looking at it the wrong way around.
There never were any gravitational forces, just
your choice of coordinate system made fictitious
forces appear; just like when you use a
merry-go-round as your reference frame you get
coriolis forces.
If gravity is a fictitious force produced by the
choice of coordinate system, in its absence (due to
a change in coordinate system) how does GR explain
motion? Test particles move on geodesics in the
absence of non-gravitational forces, but why do they
move at all? AG
Maybe GR assumes motion but doesn't explain it. AG
The sciences do not try to explain, they hardly even try
to interpret, they mainly make models. By a model is
meant a mathematical construct which, with the addition
of certain verbal interpretations, describes observed
phenomena. The justification of such a mathematical
construct is solely and precisely that it is expected to
work.
--—John von Neumann
Another problem is the inconsistency of the
fictitious gravitational force, and how the other
forces function; EM, Strong, and Weak, which
apparently can't be removed by changes in
coordinates systems. AG
It's said that consistency is the hobgoblin of small
minds. I am merely pointing out the inconsistency of the
gravitational force with the other forces. Maybe gravity
is just different. AG
That's one possibility, e.g entropic gravity.
What is gets you is it enforces and explains the
equivalence principle. And of course Einstein's
theory also correctly predicted the bending of
light, gravitational waves, time dilation and
the precession of the perhelion of Mercury.
I was referring earlier just to the transformation
to the tangent space; what specifically does it buy
us; why would we want to execute this particular
transformation? AG
For one thing, you know the acceleration due to
non-gravitational forces in this frame.
*IIUC, the tangent space is a vector space which has elements
with constant t. So its elements are linear combinations of
t, x, y, and z. How do you get accelerations from such sums
(even if t is not constant)? AG*
*
*
So you can transform to it, put in the accelerations, and
transform back.
*I see no way to put the accelerations into the tangent space
at any point in spacetime. AG*
